So i stopped playing Toribash in 2016 and yesterday i've picked up the game again, and therefore i efficiently forgot how to do most things.

In the case of me getting knocked backwards once both players do their openers, how do you reliably move towards the opponent?

I feel as this is vital to know.

Just generally grabbing on to your opponent helps to not get too far away, it would depend on the mod that you are playing.
If you're talking about openers, its good to hold all so your Tori is guaranteed not to fall over unless pushed, and from there just contract pecs or something going forward.

I'm playing Wushu/Mushu, i don't think clapping is a great idea.

theres different ways to move across the dojo, launches by putting your arms or legs in a position to push diagonally towards your opponent is one way. or if your in a far enough distance you can lean your tori forward by contracting abs and holding hips and move from their. You just got to find your style of movement.

In terms of mushu/wushu, finding correct openers that not only move you across the dojo efficiently but also give you a good hit to your opponent. Once you get out of the opener the best way to move is to find a good position to launch and knowing what direction you are going.